19. Complete the statement using the symbol < or >.  ___ 20. Add. Write the answer in lowest terms.

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hustoncmk eNotes educator| Certified Educator

For question 19, I believe you are asking 3/8 ____ 3 /(3/5).

The first step in comparing fractions is to get a common denominator.  Then you will only need to compare the numerators.

We will start with the term on the right, 3/(3/5)

The first thing you need to do is to eliminate the fraction in the denominator.  To do this you need to multiple by the recipricol of 3/5 which is 5/3.  If you are multiplying the denominator by 5/3 you also need to mulriply the numerator by 5/3.  So you would multiply (3x(5/3) )/ ((3/5)x(5/3)). The result is (15/3)/1 or 15/3 = 5

Your comparison is now 3/8 ____ 5. It can be seen that 3/8 is less than 5, without having to convert 5 to a fraction, but to compare both in fractions they would be 3/8 ___ 40/8. the 3 is less than 40, so you would need to use the < sign. 

Your correct answer is 3/8 < 3/(3/5)

For question 20, to add fractions use need a common denominator.  You have been asked to add -3/8 + -4/8.  You already have a common denominator of 8, so you need to add the numerators. -3 + -4 = -7
-3/8 + -4/8 = -7/8.  To reduce to simplest term you need to determine if the numerator & denominator have any common factors.  In this case, -7 and 8 have no common factors, so -7/8 is already in simplest terms.

I hope this explanation helps you with other problems in the future.

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